That radio receiver has a variable gain feature which causes it to turn up the gain as the transmitter gets further and further away. If the transmitter gets "infinitely" far away, as in, is OFF, the gain goes to max and it interprets just about anything as a 0 or 1, hence it starts to generate random data, literally hallucinating.

There is virtually nothing you can about that. The transmitter program is probably sending an inital prefix code over and over a number of times, knowing that the first few times will get trashed, but eventually, the radio receiver will lower its gain (now that a real signal is coming in) and eventually it get the code. In other words, the transmitting program sends about 10 bytes of some known code, say "37" hex, doesn't much matter what, and the receiving program looks for a 37, ignores all incoming data until it gets a few 37's, then the next non-37 is the true first byte of the data. Other ways to do it, but that is the gist.

So, in your case, find some valid data and then look back at what proceeds it always, that is the radio "wakeup code".